Differentiating Powers of x (AQA A-Level Mathematics): Flashcards

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Differentiating Powers of x
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Derivative of xnx^n where nRn \in \mathbb{R}

nxn1nx^{n-1}

Before differentiating, all terms must be expressed as

Powers of xx

xx in denominator before differentiating

Must convert to negative powers first

x\sqrt{x} as a power of xx

x12x^{\frac{1}{2}}

1x\frac{1}{x} as a power of xx

x1x^{-1}

3x^3\sqrt{x} as a power of xx

x13x^{\frac{1}{3}}

1xa\frac{1}{x^a} as a power of xx

xax^{-a}

Gradient of f(x)f(x) at x=ax=a

f(a)f'(a)

Rate of change with respect to xx

dydx\frac{dy}{dx} or f(x)f'(x)

Differentiating xnx^n: what happens to exponent

Multiply by nn, reduce by 1: nxn1nx^{n-1}

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